On the Fenchel–Moreau conjugate of G-function and the second derivative of the modular in anisotropic Orlicz spaces

Jakub Maksymiuk

doi:10.1007/s00526-023-02655-8

On the Fenchel–Moreau conjugate of G-function and the second derivative of the modular in anisotropic Orlicz spaces

Abstract

In this paper, we investigate the properties of the Fenchel–Moreau conjugate of G-function with respect to the coupling function c(x, A) = |A[x]2 |. We provide conditions that guarantee that the conjugate is also a G-function. We also show that if a G-function G is twice differentiable and its second derivative belongs to the Orlicz space generated by the Fenchel–Moreau conjugate of G then the modular generated by G is twice differentiable on the Orlicz space generated by G. We also investigate second-order differentiability of action functionals on anisotropic Orlicz–Sobolev spaces.

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Author (1)

Jakub Maksymiuk dr inż.
- Faculty of Applied Physics and Mathematics
- Gdańsk University of Technology

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Articles

Type:

artykuły w czasopismach

Published in:

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS no. 63,
ISSN: 0944-2669

Language:

English

Publication year:

2024

Bibliographic description:

Maksymiuk J.: On the Fenchel–Moreau conjugate of G-function and the second derivative of the modular in anisotropic Orlicz spaces// CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS -Vol. 63,iss. 2 (2024),

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